Bob Berg’s solo on “Angles”

Bob Berg’s solo on “Angles”

Klaus Frieler

Introduction

The present study attempts to reconstruct the creative processes underlyinga specific jazz solo improvisation—Bob Berg’s solo on “Angles”—using allavailable data from the musical surface as provided in the Weimar Jazz Data-base. To this end, we also try to integrate classical and computational analysismethods to gain a more complete picture than might be possible with eithermethod alone. This includes general statistical descriptions, a look at tonaland intervallic choices as well as the metrical and rhythmical design. Centralto our analysis will be an attempt to re-tell the ‘story’ of the solo with aspecial focus on playing ideas (midlevel units) and dramaturgic curves. Wealso take a closer look at the construction principles for lines, including aclassification of line types, and in conclusion investigate the usage of intervaland pitch patterns in order to arrive at a maximally complete picture of thecreative devices and processes involved.

The object under study is a solo by Bob Berg (1951—2002), who was aneminent postbop tenor sax player of Miles Davis fame. He was born inBrooklyn, New York, and of Italian-Jewish origin. Unfortunately, only verylittle information is available about his life and personality. What is known isthat he started playing saxophone at age 13 and studied at the Juilliard School,but never graduated. He became a professional musician already at the age of18 and immersed himself in the New York loft jazz scene. He also dippedbriefly into free jazz at the end of the 1960s. He was strongly influenced byJohn Coltrane and, in the 1970s, he initially shunned the then very popularfusion jazz, preferring more classical settings. From 1973 to 1976, he workedwith Horace Silver, and was part of Cedar Walton’s band from 1977 to 1981.His first record as a leader was New Birth from 1978, which featured CedarWalton on keyboards and piano. In the 1980s, Bob Berg came to the attention

2 Klaus Frieler

of Miles Davis, who included him in his famous electric band from 1984to 1987, where he became known as an eminent fusion saxophonist. Afterhe left Davis’s Band, Bob Berg diversified his interests and played postbop,fusion, and other styles in various settings and groups. In an interview from1996, he stated: “I feel pretty comfortable moving between different areas ofmusic.” Amongst others, he was a frequent collaborator with his band matefrom the Miles Davis band, guitarist Mike Stern, and with another Davisalumnus, Chick Corea, on whose Stretch label he also released several albums.After his untimely death in a tragic car accident in 2002, Berg left a musicallegacy of 12 records as a leader and 33 records as a sideman.

The piece “Angles” is a Bob Berg original from his 1993 record Enter theSpirit. The composition can be described as a typical postbop tune, witha chord progression that is halfway between tonality and modality, verymuch in the spirit of Wayne Shorter’s compositions from the 1960s. Thetheme melody is angular, which might have been an inspiration for the titleof the song. The form and chords of the theme are not maintained duringthe solos; instead, a simplified 48-bar scheme AAB of 16 bars each is used,with four chords lasting over four bars each (cf. Table 1). The tonality is notfully clear, but a tendency to A[ major can be stated, since the A sectionsstart with A[maj7 and end with E[7 and most of the chords more or less fitinto A[major. Deviations can be found in the D[7(]11) in the A and B sections,which belong to G[ major/minor, as well as in the altered G7]9 and D7alt

chords at the ends of the B sections, which do not fit into A[major and havea rather unusual falling fourth relationship. The D7alt leads back to the A[maj7

with a tritone step, and hence these two chords might be interpreted as asemitone downward shifted variant of a A[7–E[7 connection, which wouldfit better tonally. Due to the unusual chord connections, the overall loosetonality and rather long chord lengths, the solo form is located somewherebetween tonal and modal conceptions.

The tempo is rather high with 270 bpm and the rhythmic feel oscillatesconstantly between latin in the A sections and swing in the B sections. Theaccompaniment is very dense. In particular, pianist David Kikoski playing isrhythmically very accentuated, relentlessly pushing the energy, while oftenfilling the phrase gaps in Berg’s solo with rhythmical impulses. DrummerDennis Chambers employs a modern, complex and busy drum style, whilefrequently reacting to Berg as well as driving him forward.

The solo comprises 799 tones in 38 phrases and 144 bars over three choruses.Most of the tones (85.4 %) are very short on an absolute scale (i. e., absoluteduration class) which in this high tempo equals mostly the level of eighthnotes (cf. Table 2). The syncopicity, i. e., the percentage of syncopated tones, is

BOB BERG’S SOLO ON “ANGLES” 3

Table 1: General characteristics of Bob Berg’s solo on “Angles”.

Composer Bob BergRecord Enter the Spirit (1993)Personnel Bob Berg (ts), David Kiskoski (p),

James Genus (b), Dennis Chambers (dr)Tempo 270 bpmSignature 4

4

Key Mostly A[ majorForm A(16) A’(16) B(16)

4-bar chord changes throughoutChord Changes A: A[maj7 | Cm7 | D[7 | E[7 |

B: Fm7 | D[7]11 | G7]9 | D7alt |Rhythm feels (theme) A: Latin, B: SwingRhythm feels (solos) A: Latin, B: LatinLengths 799 tones

144 bars3 choruses8 phrases

Duration 127 sDensities 6.3 tones/sec

5.6 tones/bar21 tones/phrase

Metrical centroid 3+Start of phrases 42 % (beat 3)

13 % on 3+10 % on 110 % on 2+

Syncopicity 9.2 %Tessitura A[3−A[5

(36 semitones / 3 octaves)

rather low (9.4 %) compared to the average value of about 30 % in the WeimarJazz Database. This seems to be mostly due to Berg’s highly precise timing,since, due to the metrical annotation with the FlexQ algorithm syncopicityvalues in the Weimar Jazz Database are partly driven by laid-back playing andrhythmical freedom. The listening experience corroborates this conjecture,as Berg’s solo shows a very tight rhythmical performance.

4 Klaus Frieler

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Figure 1: Piano roll representation of Bob Berg’s solo. The single panels correspondto choruses. Phrases are colored alternatively; form parts are shaded with differentgray tones.

The metrical placing of tones is uniformly distributed over all eighth notepositions in the 4

4 bar (Figure 2, middle panel). Interestingly, Berg has a strongpreference for starting his phrases on and around the third beat of a bar(Figure 2, top panel; Table 1). As can be seen in Table 3, 22 of all 38 phrasesstart on beat 3, very often (ten times) also right after a chord change (seealso Figure 1 for a visual overview of the interplay of phrase lengths, formsections, and four bar units). Another interesting fact is that Berg nearlyalways continues his phrases over the changes of contrasting form sections,i. e., A2→B1 and B1→A1, but not on the transition A1→A2. The change ofrhythm between the A and B sections under an ongoing phrase has a certainsurprise effect and also contributes to the flow of the solo. The phrase endingsare more diversely distributed but tend to fall on on-beats and also on themetrically strong first and third beats of a bar (Figure 2, lower panel).

With respect to accentuation in loudness, Berg shows a certain tendency toplay (mostly in his fast lines) four eighth groups with descending loudness,starting from the strong first and third beat (Figure 3).


Table 2: Distribution of absolute and relative duration classes.

Duration Class Absolute (%) Relative (%)

very short 85.4 9.9short 12.0 78.3medium 1.9 9.4long 0.6 1.6very long 0.1 0.8

Table 3: Distribution of metrical and hypermetrical positions of phrase beginnings.

Bar phase Beat position Sum1 2 3 4

0 1 1 10 0 121 4 2 4 1 112 1 2 6 1 103 2 1 2 0 5

Sum 8 6 22 2 38

Note. Bar phase= distance in bars from a chord change / four-bar block. Beat position= beat in the bar disregarding tatumposition.

Tonal and interval choices

The overall pitch range is three octaves from A[2 to A[5, with a strong focuson the middle octave; 83 % of all tones are between A[3 and E[5 (Figure 4, top).Tonally, the pitch classes fit very well into A[major, even though G is themost common pitch class (accordingly, G4 is the most common tone), but thisis due to some repeating patterns (‘oscillations’) in the third chorus, where G4is the central tone. Looking at the pitch class distribution (Figure 4, bottom)the A[ major seems to be rather dominant, with about 84 % of all tonescoming from A[major. However, the solo makes a much more chromaticimpression during listening. This can be explained by looking at the chordaldiatonic pitch class distribution (Figure 5) and the chord-wise distribution ofnon-diatonic tones (Figure 6). There is a clear contrast between very inside,sometimes pentatonic playing on the one hand, and highly chromatic andeven outside playing on the other hand. The latter mostly takes place in thesecond half of the B sections over the altered dominant seventh chords G7]9

6 Klaus Frieler

Phrase end

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Figure 2: Metrical distribution in Bob Berg’s solo differentiated for phrase position.Top: phrase beginnings (N = 38), middle: in-phrase tones (N = 723), bottom: phraseendings (N = 38).

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Figure 3: Loudness vs. metrical positions in Bob Berg’s solo.

and D7alt, but also once on the Cm7 of the first A section in the second chorusand on the second E[7 in the second A section of the first chorus, as well as thefirst A section of the last chorus. Interestingly, and this explains why the pitchclass distribution fits so well in A[major: He often plays A[ ionian on the G7]9


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Figure 4: Pitch distribution (top) and pitch class distribution (bottom) in Bob Berg’ssolo.

and D7alt at the end of the B section (e. g., in mm. 89–91 with a long A[maj7

arpeggio). This is an interesting technique, since A[ ionian fits well with thealtered chords but also with the overall tonality. These are also the points ofhighest harmonic tension, so in some way this outside playing results mostlyfrom ignoring these odd chords in the overall harmonic progression.

Another reason for the modern sound of the solo is Bob Berg’s preference forupper structures. For example, he plays Cm over A[maj7 (mm. 2–4, mm. 65–67), Gm7 over Cm (mm. 4–7), and Fm7[5 over D[7 (mm. 8–19, mm.25–28).

8 Klaus Frieler

Table 4: Mean and median of chordal diatonic pitch classes mapped to third layers.See text for details.

Form section Chord Median Mean

A1 A[maj7 7.0 6.6Cm7 5.0 6.9D[7 5.0 6.7E[7 7.0 6.2

A2 A[maj7 7.0 7.1Cm7 7.0 6.3D[7 7.0 6.9E[7 7.0 6.3

B1 Fm7 5.0 6.3D[7]11 9.0 8.5G7]9 9.0 7.8D7alt 9.0 8.9

All 7.0 7.02

This observation can be corroborated by mapping chordal diatonic pitchclasses to third layers. This is done by mapping 1 and 3 to itself, and themappings (7, ]7, [7)→ 7, (2, [9, ]9)→ 9, (4, ]11)→ 11, and (6, [13)→ 13.Afterwards, mean and median values of the mapped chordal pitch class distri-bution are a measure for the amount of upper structures used. The resultscan be seen in Table 4, broken down by chords. The overall median is 7, i. e.,the seventh, which is right in the center of a chord’s expansion into thirds.The interval distribution is somewhat unusual, as can be seen in Figure 7.Compared to the overall interval distribution (lower panel), there are manymore tone repetitions but also a flat plateau for small descending intervals.This however can be explained by the long oscillating figures in mm. 75–81and mm. 95–108, in which similar figures are repeated very often. Theseoscillations are responsible for the unusual interval distribution, but arenevertheless very important for the solo as a whole.

Re-telling the story

The storytelling metaphor is an important aspect in jazz parlance and jazzresearch (Frieler, Pfleiderer, Abeßer, & Zaddach, 2016b) and might also bean active guiding principle for improvising jazz solos. Of course, there are


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Figure 5: Tonal choices in Bob Berg’s solo broken down for individual four-bar chords.Dark blue: diatonic pitch classes; light blue: non-diatonic pitch classes.

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Abj7 C−7 Db7 Eb7 Abj7 C−7 Db7 Eb7 F−7 Db7#11 G7#9 D7alt

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Figure 6: Outside playing in Bob Berg’s solo for each chorus. Chords are listed as theyappear in the AAB form.

10 Klaus Frieler

All Tenor Solos

Angles

−12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12

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Figure 7: Semitone interval distribution in Bob Berg’s solo (top) and in all other tenorsax solos in the Weimar Jazz Database (bottom).

no ‘real’ stories to be told in music due to the lack of denotative meanings.Nevertheless, a certain dramaturgy might be discernible, which might ormight not follow narrative prototypes (e. g., the narrative arc).

In the following sections, we will first try a re-narration of the entire solo,based on midlevel units, and then have a look at global dramaturgic shapes.

Midlevel Analysis

Midlevel analysis is a qualitative annotation system for jazz solos which areinspired by playing ideas and called ‘midlevel units’ (MLU, cf. Frieler, Pflei-derer, Abeßer, & Zaddach, 2016a). There are nine main types of midlevel units(MLU) (line, lick, melody, rhythm, expressive, theme, quote, void, fragment)with 16 sub- and 38 sub-subcategories.

In Figure 8, a piano roll representation of the solo broken down into the maintypes of MLUs is depicted. The solo transcription in Figure 17 can be foundannotated with full MLU types. Finally, in Table 6 a complete run-down ofthe sequence of MLUs in this solo is listed.

In this solo, 51 MLUs of only five main types are used: line (21), lick (11),melody (6), rhythm (6), expressive (6). 13 MLUs are glued together to form


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Figure 8: Piano roll of Bob Berg’s solo differentiated according to midlevel units.From top to bottom: expressive (red), lick (olive), line (green), melody (blue), rhythm(purple).

phrases, and 13 MLUs are derived, mostly from the immediately precedingMLU. The mean duration of all MLUs is 2.0 s or 2.75 bars.

One striking aspect about the flow of ideas in this solo is the common com-bination line→melody/expressive, often directly glued to build a phrase. Theline part is mostly of ascending type, whereas melody/expressive parts aremostly very short, just a few tones derived from major and minor triadsand with descending contours. The first instance is in mm. 9–13, where ashort sequence of four ascending Fm7[5 arpeggios is followed right awayby a simple melody from E[ mixolydian. The next instance can be foundin mm. 30–36, where a long, rather chromatic, wavy line ends in a simpleC minor melody in mm. 35–36. Another instance is in mm. 38–42, where anascending D[mixolydian ]11 line ends in an E[mixolydian melody. Shortlyafter this, in mm. 47–51, a chromatic ascending line (mm. 47–48) is seguedinto a simple A[ ionian line—right across the transition from the first tothe second chorus and then into another short C minor melody. The nextinstance is to be found in mm. 63–67. Here, an ascending E[mixolydian lineis ended by the first expressive MLU in the solo, which is constructed fromthe tones of an A[maj7 chord and which resembles the melodies in m. 51 andmm. 2–4. It is directly followed by an expression variant, with a top tone awhole step up from G5 to A5, which suggests C dorian over the underly-

12 Klaus Frieler

ing Cm7. After this instance, which is a first peak moment in the solo, theseries of longer oscillations starts. The next instance of the model is then tobe found at the beginning of the third chorus (mm. 113–117), introducedhere by a long-reaching, arpeggiated ascending line, ending in a C minortriad-based melody. An intensified variant can then be found a few bars later,in mm. 126–132, where the melody at the end is modified a bit to accommo-date the Fm7 chord. Again a few bars later, in mm. 134–136, a shortened andupwardly transposed echo follows, itself immediately succeeded by a lick,which resembles the melody in mm. 41–42. Finally, the very last phrase, inmm. 138–144, starts out with a faint echo of the oscillations from the secondchorus, and then mutates into a short chromatic passage, segueing into adiatonic ascending arpeggio which ends in a short, two-tone expressive MLU.In a way, these very last seven bars contain the whole solo and its main ideasin a nutshell, functioning somewhat as a short conclusion.

The technique of ending a line with a short melodic part, often with longertone durations, could be dubbed ‘piggy tailing’. In many solos, the ‘piggytails’ consist of only a few tones, normally one to three, which function as ashort deceleration bringing a fast line to halt. One example for a more typical‘piggy tail’ can be found in m. 124.

It interesting to look at ideas that occur only once in the solo. First, thereis a Parker-sounding lick in m. 14–15 which is glued to a piggy tail melody.Indeed, the interval sequence (−3,−4,−5,+3,−2,+1), starting on the thirdbeat in m. 14, can be found three times in the Charlie Parker Omnibook.

Then, there is a very short rhythm_single_irregular in m. 18–19, which func-tions as an interruption of a longer line, even though the MLU right beforeit is labeled lick. Without this short intermission the whole complex wouldbe just one long wavy line.

Generally, there is a shortage of short licks in this solo. Measures 24–28 presentan ascending sequence of licks, which consists of Fm7[5 arpeggios, nearly thesame as the ones in mm. 9–11, but here extended higher and played in aspecific ‘choppy’ rhythm, which transforms it into a sequence of licks. This isa good example of how the same sequence of pitches can be transformed intosomething distinctively different by only changing the rhythm—in this caseby prolonging some inter-onset intervals. After he reaches the same endpoint(E[5) as in m. 11, Berg continues with a very short and abridged version ofm. 12, which sounds as a descending answer to the ascending arpeggios.

In m. 49, in the first bar of the second chorus, when the rhythm group shiftsback from swing to latin, Berg plays his only embellishment figure in theentire solo, which vaguely recalls a pop jazz saxophone lick, but which isfully integrated in a much longer line of mixed character (cf. p. 14).


At the end of the first A section in the second chorus, in m. 60–62, thereseems to be a short black-out in the flow of the solo. First, after finishing thelong seven-bar line that started in m. 53, Berg continues with a very short lick,which is basically a transposed version of the ‘piggy tail’ of the line (m. 59).This sounds either as a bold confirmation of the preceding line, a false start ofanother line, or as a moment to gain time. After a bar-long pause, he embarksin mm. 61 and 62 on a short line, which is basically an E[9 arpeggio over theE[7 which does not sounds fully convincing, neither tonally nor in regardto phrasing. Next, as if ‘upset’ about this rather weak passage, he expressesthat anger with a short diatonic up-swing (mm. 63 and 64) right into the firstexpressive MLU in the solo, which brings G5, the highest pitch so far, heldfor over one bar.

The last one-time element in this solo can be found in mm. 86–89, where Bergplays a mixed E[/E[+ descending arpeggio with a constant eighth/dottedquarter rhythm pattern with tone repetitions (line_i_dd) over the D[7]11.From that point on, all the remaining material is in one way or anotherrelated to some preceding material.

Dramaturgy

The dramaturgy of Berg’s solo seems to be well-crafted, either intentionallyor as emerging from group interaction. The general tension curve is doublyarched. This can be seen on one hand in the event densities across the courseof the solo. In Figure 9, the number of tones of two-bar units shifted bar-wisealong the time axis and plotted against the onset of the first tone of the barunit is depicted, along with a polynomial trend. From the beginning on, theevent density increases constantly over a long stretch and then dips downat the beginning of the second chorus to increase even more towards theend of the second chorus, where the highest densities are reached with thesequences of oscillations. The third chorus then sees a slow decay, but thisdoes not mean that the intensity decreases, it is merely shifted to anotherdimension. This can be seen in Figure 10 where pitch and loudness curves of20 note windows (with a hop-size of 10 tones) are plotted against the onsetsof the windows. Both curves show an overall ascending trend—particularlythe loudness curve—with some oscillations. One sees that the pitch heightsrise quite rapidly in the first chorus but drop towards the beginning of thesecond chorus, to rise continually towards the end. In the third chorus, acertain saturation is reached, but in fact with strong oscillations, showing astark contrast (at about 100 s). All in all, a clear peak in global intensity isreached with the sequence of oscillations.

14 Klaus Frieler

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Figure 9: Event densities (number of tones) of Bob Berg’s solo for windows of twobars shifted bar-wise along the solo.

This overall dramaturgy is also reflected in Figure 8. The melody and lickMLUs appear mostly in the first chorus whereas the second chorus is dom-inated by the sequence of oscillations. The expressive MLUs appear for thefirst time at the beginning of the second chorus, and take over the role of themelody afterwards. This has an effect of intensification. The third chorus isthen built from the double sequence of line–expressive and line–line–expressive–expressive, and resolves, finally, in the epitomic phrase line–expressive at thevery end.

Line construction

The analysis of the MLU content of the solo shows that Berg utilizes dif-ferent kind of lines in his solo: diatonic lines, arpeggios, chromatic lines,and mixtures thereof. To gain further insights, we manually classified the 21line MLUs using this four-fold classification scheme and found four diatonic,three chromatic, six arpeggiated, and eight mixed lines. They indeed differwith respect to their interval content, as the distributions of frequencies ofsemitones, whole tones, and thirds show (Figure 11).

Using a similar system, we also classified line segments of seven intervals bymoving this window by four elements. Segments always start at the beginning


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Figure 10: Smoothed pitch and loudness curves for Bob Berg’s solo. Smoothing wasdone with windows of 20 tone events and a hop size of 10 tones. Trend line fittedwith a polynomial of 6th degree.

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of line MLUs. A segment is classified as ‘pentatonic’ if thirds and whole tonesaccount for more than two thirds of the intervals (i. e., five or more). It is

16 Klaus Frieler

classified as ‘arpeggio’ if thirds and larger intervals account for more than twothirds of the intervals. It is classified as ‘diatonic’ or ’chromatic’, if semitonesand whole tones account for more than two thirds of the intervals, and thendepending on whether there are more semitones (‘chromatic’) or whole tones(‘diatonic’). Finally, segments are classified as ‘mixed’ if they do not fulfillany of these criteria or if the difference between the first and second mostfrequent class is less than 0.1. In Figure 12, the sequences of segment classesare plotted for each line in the solo. The first observation is a slight preferencefor mainly pentatonic lines (e. g., lines 1, 2, 4, 9, 18), although there is anequal share of pentatonic and mixed line segments (30.0 % each). The nextcommon segment type is ‘chromatic’ (20.8 %), followed by arpeggios (13.3 %),and ‘diatonic’ 5.8 %. The length of lines ranges from 3 (line 8, 9, 11, 13) to 12segments (line 7), with a median of 5.5. For the series of segment types, noobvious patterns can be identified, except that a segment type has a strongtendency to be repeated (about 50 %), which is partly due to the constructionof our measure. Furthermore, chromatic segments tend to occur earlier ina line (mean normalized position = .45), whereas diatonic and pentatonicsegments tend to occur later (mean normalized positions of .68 and .64). Withrespect to the entire solo, however, pentatonic segments tend to occur earlier,and arpeggios tend to appear later (e. g., in the third chorus, mm. 113ff. andmm. 126ff.). All in all, Berg shows a great variability in his approach to lineconstruction.

Pattern usage

To investigate the usage of patterns in Berg’s solo, we used the partitionfunction of the melpat module in the MeloSpyGUI with all seven Berg solosin the Weimar Jazz Database as a background corpus. Since the rhythmsare rather uniformly based on eighth notes due to the abundance of lines,we only calculated interval and pitch patterns and no rhythmical patterns.For the interval domain, we extracted patterns with at least N ≥ 5 intervals,which correspond to at least six tones. For the pitch domain, we demandedN ≥ 6. For both cases, we extracted patterns that occur at least twice, butplaced no restriction on the number of solos they should appear in.

We found 147 interval patterns meeting these conditions, with a coverage of64.8 %, i. e., about two thirds of the tones in Berg’s solo are contained in aninterval pattern of at least five intervals that occur at least twice somewherein the seven Berg solos under consideration. This is the highest coverage ofall Berg solos, which have a mean coverage of 56 %. But this is partly due tothe extensive oscillations in the solo. However, when using all postbop tenor


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Figure 12: Classification of segments of seven intervals for line MLUs in Bob Berg’ssolo. Hop size is four intervals, i. e., points are separated by four notes each. chr= chro-matic, dia = diatonic, pen = pentatonic, arp = arpeggio, mix =mixed.

solos, the coverage rises to 80.7 %, which is close to the mean coverage of78.3 %.

We found 81 pitch patterns, with a coverage of 46.8 % (mean coverage acrossall Berg solos: 40.6 %). See Figure 13 for a display of interval and pitch patternsin Berg’s solo. The longest patterns are produced by the oscillations and arenot shown.

As expected, there are fewer pitch patterns than interval patterns (because apitch pattern is automatically also an interval pattern, but not vice versa). Theshorter patterns are more volatile, whereas the very long interval patterns arealso pitch patterns, which shows that they are specifically rehearsed and then

18 Klaus Frieler

Interval Pattern

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Figure 13: Interval (top) and pitch patterns (bottom) in Bob Berg’s solo on “Angles”with an effective length of at least six occurring at least twice in the seven solos byBerg in the Weimar Jazz Database. Only patterns up to an effective length of N = 18are shown, since the longest patterns are due to the oscillations.

reproduced. The shorter patterns are probably rehearsed in many differentkeys and thus can be used as building blocks, e. g., for line constructionin many different harmonic situations. To illustrate the pattern usage byBob Berg in this particular solo a little further, we produced a network ofpattern similarities for the interval patterns. To this end, we calculated editdistances between patterns. The edit or Levenshtein distance (Levenshtein,1965; Müllensiefen & Frieler, 2004) is defined as the minimum number ofeditions, deletions, and substitutions required to transform one sequenceof symbols (here: intervals) into the other. For two completely differentsequences of different length, the maximum number of operations is thelength of the longer sequence. This can be used to convert the edit distanceinto similarity values between 0 and 1. The full matrix of similarities betweenall interval patterns was then converted into an adjacency matrix using athreshold of 0.5. This means that all similarities lower than .5 were set to 0and all similarities above .5 were set to 1. These values were used to create asimilarity network by feeding them into a graph representation algorithmfrom the network package for R (R Development Core Team, 2008). Theresult can be seen in Figure 14.


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Figure 14: Network representation of all interval patterns in Bob Berg’s solo. Edgesare drawn according to pattern similarities, which were calculated using edit distanceand range from 0 to 1, where a value of 1 means identity. Only connections withsimilarity greater than 0.5 shown. Node labels are arbitrary tags assigned by thepartition algorithm.

20 Klaus Frieler

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−1,−1,−1,−1,2,2,3

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1,−1,−1,−1,−1,2,11,−2,1,−1,−1,−1,−1,2,2

−1,−1,−1,−1,2,2,−4,2,−1,−1,4,−2,−3

−1,−1,−1,−1,2,2,−4,2,−1,−1,4,−2,−4

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−1,−1,−1,−1,2,2,3,−1

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Figure 15: Close-up of the upper middle cluster of the full pattern network. Nodelabels are pattern values; edge widths are proportional to similarity.

One sees two clusters of strongly interconnected patterns and one rather loosecluster. There are also a few small cluster of only two or three highly similarpatterns as well as several singletons. To highlight the cluster structures inmore detail, we will have a closer look at the dense cluster in the upper middleof the network plot. It can be seen in Figure 15. A list of the patterns in thiscluster can be found in Table 5 and are shown in Figure 16. The pattern b12is the longest of all with 17 intervals (18 tones). It occurs twice in “Angles”(mm. 30 and 108) at the same metrical position and with identical pitches. Itconsists of a rather unpredictable sequence of mostly semi- and whole tones.Clearly, this pattern was pre-rehearsed. This is corroborated by the fact thatthe next two longest patterns, l18 and m18, are, except for their last tones,contained in pattern b12 as a suffix. On the other hand, pattern m28, apartfrom some slight rhythmical variation, is contained at the beginning of b12,as a prefix. However, it is counted as a separate pattern because it also occursin another solo by Bob Berg (on “You and the Night and the Music” from the1997 album Another Standard). The same holds true for pattern e31, which isfully contained in b12, but occurs five times in total in three different solos(there only as proper sub-patterns). All other patterns in this cluster are moreor less variations of the material from the above mentioned patterns.

The main core of this pattern cluster is the interval pattern -1, -1, -1, -1, 2, 2 offour descending semitones and two ascending whole tones, mostly realized


Table 5: Upper middle interval pattern sub-network.

Tag MM. N FC FA Value

b12 30, 108 17 2 2 -2, 1, 1, -2, 1, -1, -1, -1, -1, 2, 2, -4, 2, -1, -1, 4, -2

l18 31 13 2 1 -1, -1, -1, -1, 2, 2, -4, 2, -1, -1, 4, -2, -3m18 43, 110 13 2 2 -1, -1, -1, -1, 2, 2, -4, 2, -1, -1, 4, -2, -4m28 140 10 2 1 -1, 1, 1, -2, 1, -1, -1, -1, -1, 2v26 54 10 4 1 -1, -1, 2, -1, -1, -1, -1, -1, 2, 2e31 30, 92, 109 9 5 3 1, -2, 1, -1, -1, -1, -1, 2, 2m38 55 8 2 1 -1, -1, -1, -1, 2, 2, 3, -1a44 55, 92 7 3 2 -1, -1, -1, -1, 2, 2, 3d45 140 7 2 1 1, -1, -1, -1, -1, 2, 1s42 141 7 6 1 -1, -1, -1, 2, 1, 2, -3s43 58 7 4 1 -4, -1, -1, -1, 2, 1, 2u64 34 5 3 1 -1, -1, -1, -1, -3v64 93 5 3 1 -1, -1, -1, -1, 4

Note. Tag= pattern name generated by the partition algorithm; MM.= measuresin “Angles” where pattern can be found; FC = frequency of pattern in the entireBob Berg sub-corpus in the Weimar Jazz Database; FA = frequency of pattern inthe solo on “Angles”.

in the middle octave starting from G4 and on a strong metrical position(first or third beat, only exception: v64). Only pattern u64 contains a slightlyshorter version (last interval is a descending minor third −3). Notably, thiscore pattern does not occur as an independent pattern in the pattern parti-tion, because it is always embedded in longer patterns. The most commoncontinuation is a whole tone up (all patterns except s32 and v64), followedeither by a descending major third or an ascending minor third.

Taken together, this pattern cluster alone shows clearly that Berg has a pre-rehearsed pattern vocabulary at his disposal, which is stable over time. It ismostly fixed in metrical and pitch position but can be varied by chainingdifferent sub-patterns to longer patterns with contextual adjustments.

Creative Devices

In the foregoing sections, we provided a rich description of Berg’s solo on“Angles” using many different perspectives. We would like to summarize herethe most important creative devices that are employed by Berg.

22 Klaus Frieler

Figure 16: Interval pattern of the upper middle cluster of the full pattern network.All instances are the first instances in the solo on “Angles”.


First of all, the entire solo seems to follow a rather well-crafted dramaturgy.It shows a double arch shape with overall increasing energy. The dramaturgyseems to develop rather spontaneously and is partially driven by interactionswith the band. One characteristic of this solo is the frequent changes ofrhythm feel from latin to swing and back, which produce a tension andrelease pattern on the highest level. Berg nearly always continues his phrasesseamlessly over these changes in rhythmic feel, which adds to the flow of hisimprovisation and the impression of mastery and virtuosity.

On the level of playing ideas, the solo is characterized by an abundance oflines with a conspicuous absence of licks. Rather, the frequently long linesof variable types are contrasted with either pentatonic or diatonic melodieswhich become more expressive during course of the solo. These melodic licksoften occur at the end of a long line, and were dubbed ‘piggy tails’. Such smallextensions at the end of a longer line, or sometimes also at the beginning,can be frequently observed in jazz solos since bebop, but in this solo, theseare rather long and melodious (or expressive). Their general function mightbe to give a certain form of closure to a line and/or coming to a stop after afast-moving line. Sometimes, the effect is that the line feels like a mere upturnto its more melodious or expressive piggy tail.

As shown above, Berg constructs his lines very diversely, mixing penta-tonic/diatonic sections with (wide) arpeggios and chromaticism. These linesappear to be composed from preconceived patterns that Berg has in his vo-cabulary. Some of these patterns can be found in solos on the same recordbut also in solos played years later.

The contrast between pentatonic/diatonic material and chromatic and out-side material can be seen as a general feature of this solo. Though it is strictlyrooted in A[major, the frequent chromaticism as well as the ‘trick’ of playingthe main key over the outside harmonies D7alt and G7]9 at the end of eachchorus, i. e., essentially ignoring these chords, create tonal tension and relax-ation patterns which propel the solo forward. These parts are contrasted withmelodies of ostensible simplicity as well as with expressive outbursts. Theconstruction of lines with inside/outside elements as well as the inside vs. out-side contrasts of larger parts can be seen as a kind of self-similarity and mightresult from deliberate artistic decisions. Berg works by contrasting the simple(e. g., pentatonic, melody) with the complex (e. g., chromaticism, elaborateasymmetric lines) on different levels. This might also be reflected in anotherimportant element not only of this solo but also of many other postbop play-ers (e. g., Michael Brecker, Kenny Garrett, Chris Potter), namely the extensiveoscillating figures. These normally have an intensifying effect, especially ifplayed in ascending tonal sequences as in this solo. Compared to intricate

24 Klaus Frieler

bebop lines, these oscillations are simple in construction and rather easyto perform, hence early bebop pioneers such as Parker and Gillespie mighthave shunned them as they were used by Rhythm & Blues ‘honkers’. But theneed for heightened expressivity in the postbop style, probably starting withColtrane, (re-)introduced them into modern jazz improvisation, where theyserve as energetic counterparts to more sophisticated line constructions.

Finally, Berg frequently uses motivic relationships and tonal sequences tocreate musical logic and coherence. The use of long and very long patterns(e. g., pattern b12 and m18) and parts thereof might also contribute to a senseof coherence. Apart from a few single ideas, much of the material in this solois related in one way or another, sometimes subtly transformed and varied,sometime re-contextualized, sometimes re-used verbatim. In this regard, thevery last phrase (mm. 139–144) is remarkable as it subsumes the entire soloin a nutshell and is hence also an epitome for Berg’s coherent solo design.

Conclusion and outlook

This in-depth case study of a single solo attempts to retrace the underlyingcreative processes. As a case study, its power for generalizations is of courselimited, but a large collection of similar in-depth case studies along with large-scale contextualization in a corpus might finally converge to form a stable andgeneral model of jazz improvisation. We can state for now, however, that theresults presented here are compatible with a three-level hierarchical model.The highest level is the overall dramaturgy of the solo, created in interactionwith the band, which results in the decisions for certain playing ideas onthe middle level, e. g., lines, melodies, expressive moments, oscillations etc.,which are then—on the lowest level—realized by combining preconceivedmaterial on one hand and spontaneous out-of-the-moment inventions onthe other. However, the last point has to actually been proven yet. The sub-corpus of Berg’s solos in the Weimar Jazz Database is rather small. For thefuture, it would be highly desirable to gather a much larger collection to seewhether certain elements, such as the melodic ‘piggy tails’ and the oscillationpatterns, were indeed invented on-the-fly or whether pre- or postdecessorscan be found in Berg’s oeuvre.

Finally, the selection and pre-creation of the material, e. g., their tonal con-struction, seem to be highly specific for Berg’s personal style but are nonethe-less shaped by a general stylistic sensitivity.


Table 6: Run-down of MLUs in Bob Berg’s solo on “Angles”.

Measures MLU Scale Comment

2–3 rhythm-si G4

4–5 ~melody C-aeol

5–7 ~#melody C-aeol Gm7 arpeggios.

9–10 line-wavy-asc D[-mixo Fm7[5 arpeggios upwards inzig-zag fashion.

11–13 melody E[-mixo Melody reached after longascending line (‘piggy tail’).

14–15 ~lick E[-mixo Strong cadential effect.

16–17 lick E[-mixo Jump octave up.

18–19 ~rhythm-si F4 Short thinking pause.

19–23 ~line-wavy-desc E[-mixo/C-aeol

Mostly diatonic.

24–25 lick D[-mixo Sequence of licks as brokenversion of the Fm7[5 arps. inm. 9–10.

25 #+lick D[-mixo Three-beat pattern, metricshift.

26 #+lick D[-mixo Last tone of lick is first toneof next.

26–27 #+lick D[-mixo

27–28 #+lick D[-mixo

28 #+lick D[-mixo Last tone missing.

29 #lick D[-mixo Answers last lick, dramaticpause.

30–34 line-wavy-hor E[-mixo Largely chromatic line(‘apparatus’). Interestingchange to B section (swingfeel) in middle of line,accompanied by a registerchange.

35–36 ~melody C-aeol Line/melody with piggytail. Stark contrast.

26 Klaus Frieler

38–40 line-wavy-asc D[-mixo Recalls the D[7 arp. before.

41–42 ~melody A[-ion Line/melody with piggytail.

43–46 line-wavy-desc E[-mixo Outside.

47–50 line-wavy-asc E[-WT/A[-ion

Change to second chorusmid-line.

51–52 ~melody C-minpent Another piggy tail.

53–59 line-wavy-hor chrom →G[-majpent

Longest line.

60 #lick D[-mixo More of a fragment, echoessmall piggy tail of last line(cf. m. 29).

61–62 line-wavy-hor E[-mixo Unusually short arpeggioline.

75–78 rhythm-mr G[-majpent First oscillation. Heatingthings up a bit.

79–82 #rhythm-mr E[-mixo/A[-ion

Sequencing up first, butthen down. Ends with ashort piggy tail way up inthe sky.

83–86 line-wavy-asc A[-ion/ D[-mixo

Zig-zagging upwards.

86–88 ~line-i-dd D[-mixo Piggy tail after ascendingline, between staircase andmelody.

89–94 line-wavy-hor A[-ion Outside. Mixture ofdiatonic arps., scales, andchromatic falls.

95–100 rhythm-mr A[-ion Three-beat diatonicmordents are shortened totwo beats, highest rhythmicenergy.

101–104 #rhythm-mr C-dor Changes only A[ to A,spicing things up.

105–108 #rhythm-mr G-majpent Moving a semitone up.Possibly the peak of thesolo. Band fires up.


109–112 line-wavy-desc E[-mixo/chrom

After a clear mark by theband, Berg is going back tolines, using the apparatusfrom m. 30.

113–116 line-wavy-asc A[-majpent Far-reaching line fromA[2–A[5.

116–117 ~expressive Cm Again, a piggy tail after along ascending line, againon a C minor triad.

118–121 line-wavy-hor C-blues A rather cheesy minor bluesline.

122–124 line-wavy-desc D[-mixo Continues preceding lineafter a short stop on C/D[7.Mistake?

126–129 line-wavy-asc E[-mixo Up-swinging diatonic linewith large intervals.

129–132 ~expressive F-aeol Longest top tone in the solo.Again, line to expressivepiggy tail, with anotherpiggy tail.

134–135 expressive D[-mixo Another top tone on #11, aWT higher. Upwardsequence of expressive ideas.

135–137 ~##lick D[-mixo#11 Piggy tail of the precedingexpressive. Extendedversion of the previouspiggy tail.

138–142 #10line-wavy-hor F-minpent/D-alt

Reminiscence of the lastoscillation, but re-mixedinto a wavy line.

142–144 ~expressive D-alt Again, expressive piggy tailafter a line. Segues intotheme after this.

Note. mixo=mixolydian, min/majpent=minor/major pentatonic, aeol= aeolian,blues = blues scale, dor = dorian, WT = whole-tone scale, ion = ionian/major,arp = arpeggio, alt = altered scale, chrom = chromatic scale.

28 Klaus Frieler

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References

Frieler, K., Pfleiderer, M., Abeßer, J., & Zaddach, W.-G. (2016a). Midlevelanalysis of monophonic jazz solos. A new approach to the study ofimprovisation. Musicae Scientiae, 20(2), 143–162.

Frieler, K., Pfleiderer, M., Abeßer, J., & Zaddach, W.-G. (2016b). “Tellinga story”. On the dramaturgy of monophonic jazz solos. EmpiricalMusicology Review, 11(1). Retrieved from http://emusicology.org/article/view/4959

Levenshtein, V. I. (1965). Binary codes capable of correcting deletions,insertions, and reversals. Doklady Akademii Nauk SSSR, 163(4), 845–848. (English translation in: Soviet Physics Doklady, 10(8), pp. 707–710,1966)

Müllensiefen, D., & Frieler, K. (2004). Cognitive adequacy in the mea-surement of melodic similarity. Algorithmic vs. human judgments.Computing in Musicology, 13, 147–176.

R Development Core Team. (2008). R: A language and environment forstatistical computing. Vienna.

Documents

Bob Berg’s solo on “Angles”